A218214 Number of primes up to 10^n representable as sums of consecutive squares.

1, 5, 18, 48, 117, 304, 823, 2224, 6113, 16974, 48614, 139349

Offset

1,2

Comments

There are no common representations of two, three or six squares for n < 13, so

a(n) = A218208(n) + A218210(n) + A218212(n); n < 13.

Links

Table of n, a(n) for n=1..12.

Formula

a(n) = sum(A218213(k),k=1..n)

Example

a(1) = 1 because only one prime less than 10 can be represented as a sum of consecutive squares, namely 5 = 1^2 + 2^2.
a(2) = 5 because there are five primes less than 100 representable as a sum of consecutive squares: the aforementioned 5, as well as 13 = 2^2 + 3^2, 29 = 2^2 + 3^2 + 4^2, 41 = 4^2 + 5^2 and 61 = 5^2 + 6^2.

Mathematica

nn = 8; nMax = 10^nn; t = Table[0, {nn}]; Do[k = n; s = 0; While[s = s + k^2; s <= nMax, If[PrimeQ[s], t[[Ceiling[Log[10, s]]]]++]; k++], {n, Sqrt[nMax]}]; Accumulate[t] (* T. D. Noe, Oct 23 2012 *)

Crossrefs

Cf. A027861, A027862, A027863, A027864, A027866, A027867, A163251, A174069, A218208, A218210, A218212, A218213.

Sequence in context: A217866 A256539 A109363 * A146213 A344311 A176145

Adjacent sequences: A218211 A218212 A218213 * A218215 A218216 A218217

Keyword

nonn,base

Author

Martin Renner, Oct 23 2012

Status

approved